The Einstein-Hilbert action (and thus the dynamics of gravity) can be obtained by: (i) combining the principle of equivalence, special relativity and quantum theory in the Rindler frame and (ii) postulating that the horizon area must be proportional to the entropy. This approach uses the local Rindler frame as a natural extension of the local inertial frame, and leads to the interpretation that...

We study the survival probability and the growth rate for branching random walks in random environment (BRWRE). The particles perform simple symmetric random walks on the d-dimensional integer lattice, while at each time unit, they split into independent copies according to time-space i.i.d. offspring distributions. The BRWRE is naturally associated with the directed polymers in random environm...

An essential assumption in the Vafa and Witten’s theorem on P and CT realization in vector-like theories concerns the existence of a free energy density in Euclidean space in the presence of any external hermitian symmetry breaking source. We show how this requires the previous assumption that the symmetry is realized in the vacuum. Even if Vafa and Witten’s conjecture is plausible, actually a ...

We study several-matrix models and show that when the potential is convex and a small perturbation of the Gaussian potential, the first order correction to the free energy can be expressed as a generating function for the enumeration of maps of genus one. In order to do that, we prove a central limit theorem for traces of words of the weakly interacting random matrices defined by these matrix m...

We derive high-temperature series expansions for the free energy and the susceptibility of random-bond qstate Potts models on hypercubic lattices using a stax-graph expansion technique. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength p as well as the dimension d as symbolic par...

-A two term Ginzburg-Landau Hamiltonian for the free energy density of n-layer systems is in~roduced. It is used to derive a distribution function for such systems and to obtain scaling laws involving the number of components. We discuss the validity of this mean-field theory for stretched polymers in two-dimensional space and for fluid membranes.

We calculate the one-loop corrections to the free energy and to the entropy for fields with arbitrary spins in the space S1⊗HN . For conformally invariant fields by means of a conformal transformation of the metric the results are valid in Rindler space with D = N + 1 dimensions. We use the zeta regularization technique which yields an ultraviolet finite result for the entropy per unit area. Th...

Topological charge distributions in 2 dimensional CP 2 model with θ-term is calculated. In strong coupling regions, topological charge distribution is approximately given by Gaussian form as a function of topological charge and this behavior leads to the first order phase transition at θ = π. In weak coupling regions it shows non-Gaussian distribution and the first order phase transition disapp...

In this talk I will discuss the role of finite temperature quantum corrections in string cosmology and show that they can lead to a stabilization mechanism for the volume moduli. I will show that from the higher dimensional perspective this results from the effect of states of enhanced symmetry on the one-loop free energy. These states lead not only to stabilization, but also suggest an alterna...

We study the analyticity properties of the free energy fγ(m) of the Kac model at points of first order phase transition, in the van der Waals limit γ ↘ 0. We show that there exists an inverse temperature β0 and γ0 > 0 such that for all β ≥ β0 and for all γ ∈ (0, γ0), fγ(m) has no analytic continuation along the path m ↘ m∗ (m∗ denotes spontaneous magnetization). The proof consists in studying h...